The generation, control and transfer of triplet excitons in molecular and hybrid systems is of great interest owing to their long lifetime and diffusion length in both solid-state and solution phase systems, and to their applications in light emission(1), optoelectronics(2,3,) photon frequency conversion(4,5) and photocatalysis(6,7). Molecular triplet excitons (bound electron-hole pairs) are 'dark states' because of the forbidden nature of the direct optical transition between the spin-zero ground state and the spin-one triplet levels(8). Hence, triplet dynamics are conventionally controlled through heavy-metal-based spin-orbit coupling(9-11) or tuning of the singlet-triplet energy splitting(12,13) via molecular design. Both these methods place constraints on the range of properties that can be modified and the molecular structures that can be used. Here we demonstrate that it is possible to control triplet dynamics by coupling organic molecules to lanthanide-doped inorganic insulating nanoparticles. This allows the classically forbidden transitions from the ground-state singlet to excited-state triplets to gain oscillator strength, enabling triplets to be directly generated on molecules via photon absorption. Photogenerated singlet excitons can be converted to triplet excitons on sub-10-picosecond timescales with unity efficiency by intersystem crossing. Triplet exciton states of the molecules can undergo energy transfer to the lanthanide ions with unity efficiency, which allows us to achieve luminescent harvesting of the dark triplet excitons. Furthermore, we demonstrate that the triplet excitons generated in the lanthanide nanoparticle-molecule hybrid systems by near-infrared photoexcitation can undergo efficient upconversion via a lanthanide-triplet excitation fusion process: this process enables endothermic upconversion and allows efficient upconversion from near-infrared to visible frequencies in the solid state. These results provide a new way to control triplet excitons, which is essential for many fields of optoelectronic and biomedical research.